acker function

Pole placement gain selection using Ackermann's formula

Computes the Pole placement gain selection using Ackermann's formula.

acker(a, b, p)

Arguments

• a: State-matrix of a state-space system
• b: Input-matrix of a state-space system
• p: closed loop poles

Details

K <- ACKER(A,B,P) calculates the feedback gain matrix K such that the single input system . x <- Ax + Bu

with a feedback law of u <- -Kx has closed loop poles at the values specified in vector P, i.e., P <- eigen(A - B * K).

This method is NOT numerically stable and a warning message is printed if the nonzero closed loop poles are greater than 10

in P.

Examples

F <- rbind(c(0,1),c(0,0))
G <- rbind(0,1)
H <- cbind(1,0);
J <- 0
t <- 1
sys  <-  ss(F,G, H,J)
A  <-  c2d(sys,t);
j <- sqrt(as.complex(-1));
pc  <- rbind(0.78+0.18*j, 0.78-0.18*j)
K  <-  acker(A$A, A$B, pc)